一类变系数时滞分数阶神经网络的同步控制

Synchronization control of a class of fractional order neural networks with variable coefficients and time delays

研究一类带有Caputo分数阶导数的变系数时滞神经网络的同步问题.首先,通过将时滞及变系数引入已知的神经网络模型,得到一类能更准确地描述神经元之间相互作用的全新神经网络模型;其次,基于新的神经网络模型,提出一种简单的全局同步方案,并给出了同步控制器的解析表达式;最后,通过构造Lyapunov函数并利用时滞分数阶微分系统的Razumikhin型稳定性定理,证明了由驱动-响应系统得到的误差系统的零解稳定性,从而得到确保所研究的变系数时滞神经网络全局同步的充分条件.此外,通过数值算例验证了所得理论结果的正确性.

The purpose of this article is to research the synchronization problem of a class of variable coefficient neural networks with time delay and Caputo fractional derivative.Firstly,by introducing the time delay and variable coefficient into the known neural network model,a new neural network model that can more accurately describe the interaction between neurons is obtained.Secondly,based on the new neural network model,a simple global synchronization scheme is proposed,and the analytical expression of the synchronization controller is given.Finally,by constructing Lyapunov function and using Razumikhin type stability theorem of fractional differential systems with time delay,the stability of zero solution of the error system obtained from the drive response system is proved,thus obtaining sufficient conditions to ensure the global synchronization of the studied variable coefficient delayed neural networks.In addition,numerical examples verify the correctness of the theoretical results obtained.